A generalization of Aubry–Mather theory to partial differential equations and pseudo-differential equations |
| |
Authors: | Rafael de la Llave Enrico Valdinoci |
| |
Affiliation: | aUniversity of Texas at Austin, Department of Mathematics, 1 University Station, C1200, Austin, TX 78712-0257, USA;bDipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 1, I-00133 Roma, Italy |
| |
Abstract: | We discuss an Aubry–Mather-type theory for solutions of non-linear, possibly degenerate, elliptic PDEs and other pseudo-differential operators.We show that for certain PDEs and ΨDEs with periodic coefficients and a variational structure it is possible to find quasi-periodic solutions for all frequencies. This results also hold under a generalized definition of periodicity that makes it possible to consider problems in covers of several manifolds, including manifolds with non-commutative fundamental groups.An abstract result will be provided, from which an Aubry–Mather-type theory for concrete models will be derived. |
| |
Keywords: | Aubry– Mather theory Quasi-periodic solutions Calculus of variations Comparison Possibly degenerate and fractional operators Subordination Gradient flow |
本文献已被 ScienceDirect 等数据库收录! |
|